ATLANTA — Moments after scoring his second touchdown in Sunday’s NFC Championship Game, Frank Gore turned to face the deflated Georgia Dome crowd and began the first few steps of the “Dirty Bird,” the celebration dance popularized by the hometown Falcons in the late 1990s.

Then, in a move he’d practiced many times, Gore stopped and gave the crowd a dismissive wave, as if to say, “Never mind.”

“I told myself, if I get a touchdown, I’m going to start it off and try to mess it up,” Gore said after San Francisco’s 28-24 victory, one that sends the 49ers to their first Super Bowl since the 1994 season, “then tell Falcons fans, ‘Well, forget it. It’s our time.’ “

It is the 49ers’ time. The team that came one win from the NFL’s biggest stage last season is heading to New Orleans, where it will face Baltimore in Super Bowl XLVII.

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Once Super Bowl regulars who are 5-0 in those appearances, the 49ers haven’t tasted that type of success for a long time. From 2003 to 2010, they failed to qualify for the playoffs. Justin Smith was asked after the game if there was a time he thought he might never get this far.

They do, indeed, thanks to Gore’s two touchdowns — including the game-winner with 8:23 remaining for San Francisco’s first lead — and a big-play defense that prevented Atlanta from another stirring comeback like it had last week against the Seahawks.

On fourth down with 1:13 to go, Atlanta’s Matt Ryan attempted a pass over the middle to Roddy White that would have been enough to keep the drive going.

But linebacker NaVorro Bowman stuck a hand in to knock it away with 1:13 remaining.

“Everybody does a little,” 49ers coach Jim Harbaugh said, “and it adds up to be a lot.”

Harbaugh’s second-year quarterback, Colin Kaepernick, didn’t get a chance to show off his bicep-flexing touchdown celebration with a rushing touchdown. He gained just 21 yards on the ground on two attempts.

But he shredded the Falcons through the air by completing 16 of 21 for 233 yards, including a 4-yard touchdown to Vernon Davis, and had them so worried about his running ability out of the spread option that Gore and LaMichael James had plenty of room.

Gore’s fourth-quarter touchdown capped the biggest comeback victory in an NFC Championship Game. The previous NFC record was 13 points — Atlanta’s victory over Minnesota in the 1999 title game, which sent the Falcons to what remains the only Super Bowl in franchise history.

“I kind of figured that coming in and they showed that on film, so I assumed Frank and LaMichael were going to have a big day,” Kaepernick said. “Frank ran hard today, and I can’t say enough about him.”